The analysis of control systems with a high potential for robust stability on the control object output

  • М. А. Beisenbi L.N. Gumilyov Eurasian National University
  • Zh. O. Basheyeva L.N. Gumilyov Eurasian National University

Abstract

This paper considers control systems with an increased potential for robust stability in the outputof an object in the class of one-parameter structurally stable mappings from catastrophe theory.The actual problem is the design of control systems that provide in some sense the best protectionagainst uncertainty in the knowledge of the properties of an object and the instability of controlsystems. The ability of a control system to maintain stability under parametric or non-parametricuncertainty is understood as the robustness of the system. In the general formulation of thestudy of the system for robust stability, it is necessary to indicate the restrictions applied to thefluctuation of uncertain parameters of the control system, under which stability is maintained. Alarge number of papers have been devoted to the problem of studying robust stability of controlsystems. The study of the dynamic compensator with a high potential for robust stability isperformed by the gradient-velocity method of Lyapunov vector functions. The area of robuststability of the control system for the object output is obtained in the form of a system of thesimplest inequalities for the matrix of controller parameters and the monitoring device. Theproposed gradient-velocity method of Lyapunov vector functions in the study of the outputcontrol system of the object eliminates complex and ambiguous calculations and canonicaltransformations and allows one to determine the region of choice of controller parameters and theobserver, providing the desired transition characteristics of a closed system.

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Published
2019-10-28
How to Cite
BEISENBI, М. А.; BASHEYEVA, Zh. O.. The analysis of control systems with a high potential for robust stability on the control object output. Journal of Mathematics, Mechanics and Computer Science, [S.l.], v. 103, n. 3, p. 19-30, oct. 2019. ISSN 2617-4871. Available at: <https://bm.kaznu.kz/index.php/kaznu/article/view/650>. Date accessed: 22 oct. 2020. doi: https://doi.org/10.26577/JMMCS-2019-3-23.
Keywords Control Systems, Closed-Loop Control Systems, Lyapunov Vector Function, Gradient-Speed Method